In this Letter a first-order Lagrangian for the SchrödingerNewton equations is derived by modifying a second-order Lagrangian proposed by Christian [Exactly soluble sector of quantum gravity, Phys. Rev. D 56(8) (1997) 48444877]. Then Noether's theorem is applied to the Lie point symmetries determined by Robertshaw and Tod [Lie point symmetries and an approximate solution for the SchrödingerNewton equations, Nonlinearity 19(7) (2006) 15071514] in order to find conservation laws of the SchrödingerNewton equations. © G. Gubbiotti and M. C. Nucci.
Conservation laws for the Schrödinger-Newton equations / G. Gubbiotti, M.C. Nucci. - In: JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS. - ISSN 1402-9251. - 19:3(2012 Sep), pp. 1220002.292-1220002.299. [10.1142/S1402925112200021]
Conservation laws for the Schrödinger-Newton equations
G. GubbiottiPrimo
;
2012
Abstract
In this Letter a first-order Lagrangian for the SchrödingerNewton equations is derived by modifying a second-order Lagrangian proposed by Christian [Exactly soluble sector of quantum gravity, Phys. Rev. D 56(8) (1997) 48444877]. Then Noether's theorem is applied to the Lie point symmetries determined by Robertshaw and Tod [Lie point symmetries and an approximate solution for the SchrödingerNewton equations, Nonlinearity 19(7) (2006) 15071514] in order to find conservation laws of the SchrödingerNewton equations. © G. Gubbiotti and M. C. Nucci.
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